SOLUTION: A plane reaches 1200 Km 1 hr earlier, if the speed of the plane is increased by 60km/hr from its initial speed. what is the initial speed of the plane?

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Question 205849: A plane reaches 1200 Km 1 hr earlier, if the speed of the plane is increased by 60km/hr from its initial speed. what is the initial speed of the plane?
Answer by AndrewRyan(3) About Me  (Show Source):
You can put this solution on YOUR website!
(x+60) [(1200/x)-1] = 1200
1200 - x + (72000/x) - 60 = 1200
x(1200 - 60 - x + (72000/x) = 1200)
1140x - x^2 + 72000 = 1200x
-x^2 + 1140x - 1200x + 72000 = 0
-x^2 - 60x + 72000 = 0
x^2 + 60x - 72000 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B60x%2B-72000+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2860%29%5E2-4%2A1%2A-72000=291600.

Discriminant d=291600 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-60%2B-sqrt%28+291600+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2860%29%2Bsqrt%28+291600+%29%29%2F2%5C1+=+240
x%5B2%5D+=+%28-%2860%29-sqrt%28+291600+%29%29%2F2%5C1+=+-300

Quadratic expression 1x%5E2%2B60x%2B-72000 can be factored:
1x%5E2%2B60x%2B-72000+=+1%28x-240%29%2A%28x--300%29
Again, the answer is: 240, -300. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B60%2Ax%2B-72000+%29

(x - 240)(x + 300)
x = 240; x = -300 [-300 will be ignored because there is no negative speed]
x = 240
checking:
(240+60) [(1200/240)-1] = 1200
(300) (5 - 1) = 1200
(300) (4) = 1200
1200 = 1200
x = 240 is a solution